By himself entertainment (if you want to call rolling rocks entertainment) is different than walks and structured playtime/exercise. He is mentally bored. Walks provide mental stimulation as does training. Also do YOU go out and play with him?? Him rolling rocks sounds like he's bored honestly. My dogs play in the house alone at times, but I also go out there with them and play. Throw a ball and have them bring it back, take them on walks so they can see the world, hide objects and have them find them, STUFF kongs with food so they have to work to get the food out. Again you want to provide physical exercise but also mental stimulation and rolling a rock around the yard isn't mental stimulation. Dogs are like kids you need to interact with them otherwise they become bored.
Have you thought about crate training him while you are gone? Many of the issues you have can be trained out through exercise, mental stimulation, as well as formal training (either training them yourself or via the help of a professional), but you have gone to WAY too much trouble to "dog proof" your home. My trashcan is in my laundry room only because that's the only place it fits, there is no lid, my dog goes in there sometimes if I leave the door open and he sometimes sniffs but he does not bother because he knows better. The cat food I started training him to stay out of it. I still do not let him near it without human supervision just because he gets the runs if he eats it and I don't quite trust him 100% yet by it without a correction but he hasn't bothered it at all in a couple of months, same with our cat box, I do have a booda dome, partially to keep the dogs out of it (mainly my dog that passed away), but for the smell and litter mess as well, and we have created a barrier tha he is not allowed past the threshold of the bathroom doorway where it is (same with the cat food).
TRAINING TRAINING TRAINING lots of mental stimulation and structured exercise, whether it be off leash with you playing WITH him or on leash taking him for walks, but putting him in the backyard and letting him entertain himself with rocks is kind of sad. It's like putting a human child in the backyard all by themselves and saying "here's a soccer ball go play"...all by themselves. Kids want to interact with you, play WITH you, have fun WITH you, dogs aren't much different. I kick a ball around the yard WITH my dog, if I get tired and he's still raring to go I'll switch to throwing it and he brings it back, we do leashed walks, we do training, all of this daily. Does it take an extra 2 hours or so of my day? Yep, but my dog (who is still a puppy mind you) doesn't destroy anything, doesn't get into trash, doesn't chew on things he shouldn't, doesn't have separation anxiety (this is a human created behavior it is not a normal natural dog behavior BTW), doesn't have fear, aggresstion, or any other behavioral problems. He is by no means a perfect dog, but I DO notice he starts doing things he shouldn't on days when it rains and he can't have as much interaction playtime, those days I stuff Kongs, or hide things around the house for him to search for, things that work his mind.
I truly think a lot of your issues can be solved with more interactive and structured exercise and some serious training.
And you never know, dogs that have had "hard lives" can very possibly live long lives. That's no reason to not try to make his time with you happy and fullfilling as a dog being a dog.
Good luck!